Field Theory and Quantitative Models for Pedestrian Dynamics

In the original papers of K. Lewin we find a mathematical model of human behavior. The basic concepts are a topological space and vectors leading to the hodological space. The model is non-quantitative. The aim of this paper is to present a down to the earth analysis of the differences between the non-quantitative model and quantitative models. From an empirical point of view (event management) we discuss quantitative instances of the model, including the social forces model. Some comments to the geometry of other models are also presented.